Results 51 to 60 of about 14,447 (145)

Pseudoprime Reductions of Elliptic Curves [PDF]

open access: yesCanadian Journal of Mathematics, 2012
Abstract Let E be an elliptic curve over ℚ without complex multiplication, and for each prime p of good reduction, let nE(p) = |E(𝔽p)|. For any integer b, we consider elliptic pseudoprimes to the base b. More precisely, let QE,b(x) be the number of primes p ⩽ x such that bnE(p) ≡ b (mod nE(p)), and let πpseuE,b (x) be the number of compositive nE(p ...
David, Chantal, Wu, J
openaire   +5 more sources

ED25519: A New Secure Compatible Elliptic Curve for Mobile Wireless Network Security

open access: yesJordanian Journal of Computers and Information Technology, 2022
Wireless Sensor Networks (WSNs) create various security threats such as application variance in different sectors along with the model of cryptographic primitive and necessity.
MAUSAM DAS, Zenghui Wang
doaj   +1 more source

ELLIPTIC-CURVE CRYPTOGRAPHY (ECC) AND ARGON2 ALGORITHM IN PHP USING OPENSSL AND SODIUM LIBRARIES

open access: yesInformatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska, 2020
This paper presents the elliptic-curve cryptography (ECC) and Argon2 algorithm in PHP using OpenSSL and Sodium cryptographic libraries. The vital part of this thesis presents an analysis of the efficiency of elliptic-curve cryptography (ECC) and the ...
Mariusz Duka
doaj   +1 more source

Elliptic Curve Lightweight Cryptography: A Survey

open access: yesIEEE Access, 2018
Since it was invented in 1986, elliptic curve cryptography (ECC) has been studied widely in industry and academy from different perspectives. Some of these aspects include mathematical foundations, protocol design, curve generation, security proofs ...
Carlos Andres Lara-Nino   +2 more
doaj   +1 more source

Improved and Provably Secure ECC-Based Two-Factor Remote Authentication Scheme with Session Key Agreement

open access: yesMathematics, 2022
The remote authentication scheme is a cryptographic protocol incorporated by user–server applications to prevent unauthorized access and security attacks.
Fairuz Shohaimay, Eddie Shahril Ismail
doaj   +1 more source

On 12-congruences of elliptic curves

open access: yesInternational Journal of Number Theory, 2023
We construct infinite families of pairs of (geometrically non-isogenous) elliptic curves defined over [Formula: see text] with [Formula: see text]-torsion subgroups that are isomorphic as Galois modules. This extends previous work of Chen and Fisher where it is assumed that the underlying isomorphism of [Formula: see text]-torsion subgroups respects ...
openaire   +3 more sources

Nested Method for Optimizing Elliptic Curve Scalar Multiplication [PDF]

open access: yesEngineering and Technology Journal, 2017
The algebraic curve that attracted considerable interest in recent years is called Elliptic Curve (EC). This is due to the computational complexity of its arithmetic over a finite field.
N. Ghanim, M. Magamiss
doaj   +1 more source

Murmurations of Elliptic Curves

open access: yesExperimental Mathematics
27 pages, 16 figures, 2 ...
He, Yang-Hui   +3 more
openaire   +2 more sources

COHERENT SYSTEMS ON ELLIPTIC CURVES [PDF]

open access: yesInternational Journal of Mathematics, 2005
In this paper we consider coherent systems (E,V) on an elliptic curve which are α-stable with respect to some value of a parameter α. We show that the corresponding moduli spaces, if non-empty, are smooth and irreducible of the expected dimension. Moreover we give precise conditions for non-emptiness of the moduli spaces.
Herbert Lange, Peter E. Newstead
openaire   +3 more sources

An Efficient Signature Scheme From Supersingular Elliptic Curve Isogenies

open access: yesIEEE Access, 2019
Since supersingular elliptic curve isogenies are one of the several candidate sources of hardness for building post-quantum cryptographic primitives, the research of efficient signature schemes based on them is still a hot topic.
Yan Huang   +3 more
doaj   +1 more source

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